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It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.<\/jats:p>","DOI":"10.1115\/1.4043042","type":"journal-article","created":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T08:40:13Z","timestamp":1551602413000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":3,"title":["C2 Continuous Blending of Time-Dependent Parametric Surfaces"],"prefix":"10.1115","volume":"19","author":[{"given":"Xiangyu","family":"You","sequence":"first","affiliation":[{"name":"Faculty of Science and Technology, Bournemouth University, Talbot Campus, Poole BH12 5BB, UK e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Tian","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Bournemouth University, Talbot Campus, Poole BH12 5BB, UK e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Tang","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Bournemouth University, Talbot Campus, Poole BH12 5BB, UK e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2019,6,3]]},"reference":[{"key":"2019100601222654700_CIT0001","first-page":"65","article-title":"Constant-Radius Blending in Solid Modeling","volume":"3","author":"Rossignac","year":"1984","journal-title":"Comp. 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